path: root/Stoichiometry_And_Process_Calculations/ch7.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 7 :  Solutions and Phase Behaviour"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.1 pageno : 155"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "Pas = 71.2                      #kPa n-heptane\n",
      "Pbs = 48.9                      #kPa toluene\n",
      "P = 65.                         #kPa equilibrium\n",
      "\n",
      "# Calculation \n",
      "#P=(Pas-Pbs)*xa+Pbs,xa=mole fraction of n-heptane,liq. condition,therefore\n",
      "xa = (P - Pbs)/(Pas - Pbs) \n",
      "#ya = Pa / P , Vapour condition\n",
      "ya = Pas * xa / P \n",
      "P1 = xa * 100 \n",
      "P2 = ya * 100 \n",
      "\n",
      "# Result\n",
      "print \"Percentage of hepatne in liquid = %.1f %%\"%P1\n",
      "print \"Percentage of hepatne in vapour = %.1f %%\"%P2\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Percentage of hepatne in liquid = 72.2 %\n",
        "Percentage of hepatne in vapour = 79.1 %\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.2 pageno : 155"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "P1 = 100.               #kPa ( Vapour pressure of liq A )\n",
      "P2 = 60.                #kPa ( Vapour pressure of liq B )\n",
      "T = 320.                #K\n",
      "\n",
      "# Calculation \n",
      "#Pa = xa * P1 = 100 * xa\n",
      "#Pa = xb * P2 = 60 * xb\n",
      "#P = xa * P1 + ( 1 - xa )* P2\n",
      "# = 100xa + ( 1 - xa )* 60\n",
      "# = 60 + 40*xa\n",
      "#ya = Pa / P\n",
      "#0.5 = 100*xa / ( 60 + 40 * xa)\n",
      "xa = 60 * 0.5 / (100 - 20) \n",
      "Per1 = xa * 100 \n",
      "\n",
      "# Result\n",
      "print \"(a)Percentage of A in liquid = \",Per1,\"%\"\n",
      "Ptotal = 60 + 40 * xa \n",
      "print \"(b)Total pressure of the vapour = \",Ptotal,\"kPa\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Percentage of A in liquid =  37.5 %\n",
        "(b)Total pressure of the vapour =  75.0 kPa\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.3 pageno : 156"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "xa = 0.25          # liquid mixture\n",
      "xb = 0.30 \n",
      "\n",
      "# Calculation \n",
      "xc = 1 - xa - xb \n",
      "Ptotal = 200.                   #kPa\n",
      "Pcs = 50.                       #kPa(Vapour pressure of c)\n",
      "Pc = xc * Pcs                   #(partial pressure of c)\n",
      "yc = Pc / Ptotal \n",
      "yb = 0.5 \n",
      "ya = 1 - yb - yc \n",
      "per1 = ya * 100 \n",
      "\n",
      "# Result\n",
      "print \"Percentage of A in vapour = \",per1,\"%\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Percentage of A in vapour =  38.75 %\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.4 pageno : 156"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "P = 101.3                       #kPa flash vaporization\n",
      "Pbs = 54.21                     #kPa pressure\n",
      "Pas = 136.09                    #kPa temperature\n",
      "xf = 0.65                       # liquid mixture\n",
      "\n",
      "# Calculation \n",
      "xw = (P - Pbs)/(Pas - Pbs) \n",
      "yd = xw * Pas / P  \n",
      "# f = ( xf - xw ) / ( yd - xw )\n",
      "f = ( xf - xw ) / ( yd - xw ) \n",
      "per1 = f * 100\n",
      "\n",
      "# Result \n",
      "print \"mole percent of the feed that is vapourised = %.1f %%\"%per1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mole percent of the feed that is vapourised = 37.9 %\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.5 pageno : 157"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "from matplotlib.pyplot import *\n",
      "from numpy import zeros\n",
      "\n",
      "# variables \n",
      "T = [371.4, 378 ,383 ,388, 393, 398.6]\n",
      "Pas = [101.3, 125.3, 140 ,160, 179.9, 205.3]\n",
      "Pbs = [44.4, 55.6, 64.5, 74.8, 86.6, 101.3]\n",
      "Ptotal = 101.3                      #kPa\n",
      "\n",
      "# Calculation \n",
      "x = zeros(6)\n",
      "y = zeros(6)\n",
      "for i in range(6):\n",
      "    x[i] = (Ptotal - Pbs[i])/(Pas[i] - Pbs[i]) \n",
      "    y[i] = x[i] * Pas[i] / Ptotal \n",
      "\n",
      "# Result\n",
      "#subplot(2,1,1)\n",
      "plot(x,T,'-o') \n",
      "plot(y,T,'-x') \n",
      "suptitle(\"Boiling point diagram\")\n",
      "xlabel(\"Mole fraction, x or y\")\n",
      "ylabel(\"Temperature, K\")\n",
      "show()\n",
      "\n",
      "\n",
      "# part 2\n",
      "\n",
      "# variables \n",
      "T = [371.4, 378, 383, 388, 393, 398.6]\n",
      "Pas = [101.3, 125.3, 140, 160, 179.9, 205.3]\n",
      "Pbs = [44.4, 55.6, 64.5, 74.8, 86.6, 101.3]\n",
      "Ptotal = 101.3                                      #kPa\n",
      "x = zeros(6)\n",
      "y = zeros(6)\n",
      "\n",
      "# Calculation \n",
      "for i in range(6):\n",
      "    x[i] = (Ptotal - Pbs[i])/(Pas[i] - Pbs[i]) \n",
      "    y[i] = x[i] * Pas[i] / Ptotal \n",
      "\n",
      "w = x \n",
      "# Result\n",
      "#subplot(2,1,2)\n",
      "plot(x,w) \n",
      "plot(x,y,'-o')\n",
      "suptitle(\"Equilibrium curve\")\n",
      "xlabel(\"x, mole fraction in liquid\")\n",
      "ylabel(\"y, mole fraction in vapour\")\n",
      "show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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o0aJZCppdUiRyn6Cg8WzdOuUxj7/L5s2TdUhkWWZlZt0v6xi7fSyJqYks7rCY\nsLNhUiBErmaxges5c+bQo0cPBg8eDMD169fp0KHD0ycU+daDB49fcT4pKX/23dsYbOju2Z3TQ08z\nuN5ggr8OJjE1ERtDPh2YEQXaE/9VL1iwgH379lHsf/Mdq1atyh95caNkYTGOjo/f4u7UKRNXrlg5\njBXdT77P1XtXOfzaYSJjI3nu0+dYc3KNtHRFvvLEIuHg4JBuQT+z2UxycrJFQ4m8ZfjwNri7j0v3\nWLVqY2nRojW+vtqmRiaTTuEs5OExiLoV6hLZNxI/Vz8mhU8iaGUQZ+PO6h1RiBzxxDGJoUOHUr58\neZYvX85nn33GwoULqVixIh9//LG1MqYjYxK5U1hYBHPnbiMpyRYnJxPDhrUmOLgZp07BgAHafhWL\nFmn3WuQHYWfDaFK5ySOzm3bF7OLCHxeYtnsag+sP5h3/d3C2d9YxqRAaiw1cm0wm5s2bx9atWwEI\nCgpiyJAh2Og0MV6KRN5jNsOSJTBunLYO1HvvQaFCeqeyrNi7sYzaMorDVw8zt+1cmRYrdGeRImEy\nmfDx8eHkyZPZCpeTpEjkXdevazffHTwIn30GrVvrncjytl7YypBNQ/Aq68Xs/8ym8jOV9Y4kCiiL\nzG6ytbWlRo0aXMnPo4/CasqV01aS/fRT6N9fuxHvxg29U1lWG/c2/DzoZ+qUq0OdhXWYsWcGySYZ\n0xN5xxO7m5o2bUp0dDQNGjSgcGFtoTODwcCGDRusEvCfpCWRP/z5J0ycCMuXwwcfwCuvwENbluRL\nF25fYNiPw4i5E8P84PkEuAXoHUkUIBYbkwgPD3/s4wEBAU99spwgRSJ/iY7WWhVFimhdUDVr6p3I\nspRSfHf6O0ZsHkFzt+Z81PojXIq46B1LFACy6ZDIs0wmrQtq8mQYPhxGjwYdt1G3ivvJ95m8azJL\njy5lYvOJDKw3UBYOFBZlsSJRpEiRtK1Lk5OTSUlJoUiRIty9ezdrSbNJikT+dfkyDB0K585p02X9\n/fVOZHknb5xk8KbB/Jn8J/OD59OgYgO9I4l8yiotCbPZTFhYGPv27WP69OlPfbKcIEUif1MKvv1W\na1G0awczZkCJEnqnsiylFCuPr+Ttn97m+ZrPM63lNEo45/M/WlidVTYdsrGxoUOHDmzevPmpTyRE\nZhgM8MILcPIk2NuDpyeEhmrFI78yGAz0rt2bXwb/go3BhlrzavHl0S/lw5DIFZ7Ykli/fn3a92az\nmaioKLaA7HsVAAAgAElEQVRs2UJ0dLTFwz2OtCQKlshIbWC7UiVty1Q3N70TWd7hq4cZFDYIZztn\n5gfPx6usl96RRD5gse6mV155JW1MwsbGBldXVwYOHEj58uWzljSbpEgUPCkp8NFH8PHHMGYMvP66\nttFRfmYym1gUtYj3wt/jldqvMCFgAkUciugdS+RhFisSe/bswf8fI4h79+6lSZMmT32ynCBFouA6\nfx4GDoTbt7WB7Xr19E5keb/f/523f3qbnRd3MitoFi/UeiHtQ5sQT8NiRaJOnTocOXIk3WO+vr4c\nPXr0qU+WE6RIFGxKwcqV8NZb0KOHNm1Wp/2vrGpXzC4GbxpM5WcqM7ftXKqXrK53JJHHZPW9M8NG\ne2RkJPv27ePGjRvMnDkz7eAJCQk8ePAg60mFyAaDAXr3hrZttULh6aktRZ7f98Fq7tacowOO8sn+\nT/D73I9hDYYx2n80TnZOekcT+VyGs5uSk5O5d+8eJpOJe/fucf/+fe7fv4+joyPffPNNpg6elJRE\n/fr1MRqN1KhRg5EjRwJad5Wvry9eXl7Url2bffv2ARATE4OzszNGoxGj0Zi2G54Q/1S6NCxbBl98\nAW+8AV27wtWreqeyLHtbe95q8hbRA6I5fuM4XvO92HxeZhoKC1NPcPHixSc95V8lJCQopZRKSUlR\nDRs2VDt27FD+/v5q8+bNSimlNm3apPz9/dPO5eXl9a/Hy0RkUcAkJio1frxSpUsrNX++UiaT3oms\nI+xsmKo2u5rquqaruhx/We84IpfL6nvnE++TcHR0ZNiwYbRp04bAwEACAwNp0aJFpouQs7O24Upy\ncjImk4myZcvi6upKfHw8AHfu3KFKlSpZKnBCADg5aWMT4eHaeIW/P5w4oXcqy2v3bDtODDqBR2kP\nfD/z5aN9H5FiStE7lshnnlgkQkJCqF27NpcuXWLixIlUq1aNek8xrcRsNuPr64uLiwuBgYF4enry\nwQcf8MYbb1C5cmXeeuutdHdvx8TE4OvrS+PGjdmxY0fW/ipRIHl6wu7d8PLLEBgIY8dCYqLeqSzL\n2d6ZSYGTiOwbybZft2FcaGT3b7v1jiXykSfObvL29ubnn39O+y9Aw4YNOXDgwFOdKD4+nqCgID74\n4AOmTJnCkCFD6Ny5M2vXrmXRokVs27aN5ORkkpKSKFasGNHR0bRv356TJ09SvPjfW0QaDAYmTJiQ\n9nNAQIBuK9KK3OvaNe1+iqgoWLgQWrbUO5HlKaVYf2o9I7eMpGXVlnzY+kPKFi6rdyyhk/Dw8HSr\neE+aNClrM0Of1B/VoEEDpZRSzZs3V2FhYSoqKkpVrlw5S31b77//vpo+fboqXLhw2mNmszndzw9r\n06aNioyMTPdYJiILkWbjRqUqV1aqd2+lbtzQO4113E26q97Y8oYq82EZteDQApVqStU7ksgFsvre\n+cTupvHjx3P37l1mzpzJlClT6NevH5988kmmClBcXBz37t0DIDExkW3btuHl5UWVKlXYtWsXADt2\n7KBq1aoA3L59G7PZDGjdTidOnKB6dZkPLrIuOFhbB6p0afDygi+/zN/rQAEUdSzKR20+YvtL21l5\nfCWNlzYm6mqU3rFEXvVvFcRkMqmZM2dmqfoopdTx48eVr6+vql27tqpZs6aaNGmSUkqpvXv3qtq1\naysPDw9lNBrVgQMHlFJKrVu3Tnl6eipvb2/l5eWl1q1b98gxnxBZiAwdPqxUnTpKtWih1Nmzeqex\nDpPZpJZFL1Mu/3VRQ8OGqj8S/9A7ktBJVt87nzgm0ahRIyIjI61TsTJB7rgW2ZGaCnPnwtSp2pjF\n22+Dg4PeqSzvduJt3vnpHX44+wMftv6Q//P+P1neo4Cx2LIcI0eOxGw207VrVwoXLoxSCoPBQJ06\ndbIcNjukSIic8NtvMGQIXLyorQOl01JkVncg9gCDwgZRzLEY84Pn41HGQ+9IwkosViQCAgIe+4lj\n586dT32ynCBFQuQUpWDdOq1F0bEjTJ8OD02ky7dMZhMLDi9g0q5J9DX25d1m71LYobDesYSFyR7X\nQmTRnTvaEuQ//ACffKIt8VEQemKu37/Om1vfZPel3cz+z2w61ewkXVD5mMWKxJUrVxg9ejS///47\n27Zt48yZM+zatYv+/ftnOWx2SJEQlrJ3r7bBUdWq2qKBBWUhgJ0XdzJ402DcS7gzp+0cqpWopnck\nYQEW2760V69edOjQgd9//x0Ad3d35syZ8/QJhcjlmjSB6Gho1Ajq1oWZM7WB7vwusGogxwYew7+y\nPw0WN2BKxBQepMpKz0LzxCIRFxdHSEgItra2ANjZ2WGX37cFEwWWgwOMGwf79sHGjdCwIfxjO5V8\nycHWgTH+Yzjc/zCHrx7Ge4E32y5s0zuWyAWeWCQKFy5MXFxc2s/R0dE4OjpaNJQQeqtRA7Zvh+HD\ntb0r3ngD7t/XO5XluRV347se3/Fxm4/pv7E/Pdb14Oq9fL4Gu/hXTxyTiIyMZOjQoZw/fz5tob+1\na9dSv359a2VMR8YkhLXdvKkViYgIbawCIpgzZysPHtjh6JjK8OFtCA5upnfMHJeQksC03dP47PBn\njG82nmolqtGsSjOKO/09BexO0h32XtpLcI1gHZOKzLDo7KaUlBSOHz+OUgofHx8cdLz7SIqE0MtP\nP0Hv3hHcu7eFP/+cmva4u/s4Zs8OypeFAuDMrTMM2TSE6/evU7NUTZZ0WkJxp+LcSbrDuO3jmNpy\narrCIXInixWJhIQEZs+ezZ49ezAYDPj7+zNixIi0fSKsTYqE0FPr1uP56acpjzweFPQumzdP1iGR\ndSilCD0ZysgtIynhVILQrqF8dvgzKRB5iMVmN3Xv3p2LFy/y5ptvMmrUKC5evEi3bt2yFFKIvC4l\n5fGTNpKSbK2cxLoMBgM9vHpweshparvUxuczH7p4dJECUQA8cZpSTEwMGzduTPu5RYsWeHl5WTSU\nELmVo+Pj58T+/rsJsxlsnvixK29TKEo6l2Rqi6kEfx3Mis4r6OrRVe9YwoKe+E+6Tp06HDx4MO3n\nQ4cO6bZukxB6Gz68De7u49I9VqnSWKA1AQFw7pwusazi4TGIsU3H8m33b3n5u5eZuHOidAHnY08c\nk3juuec4e/YslSpVwmAwcOnSJWrWrImdnR0Gg4Hjx49bKysgYxJCf2FhEcydu42kJFucnEwMG9aa\n//ynGXPnwpQp2rapI0aAbT7rgQo7G0aTyk3SdTGdvHGS50Ofp16FeizpuIRC9oV0TCj+jcUGrmNi\nYv71AG5ubk990uyQIiFys/PnoW9fSEmBpUvhuef0TmR5iSmJDNg4gJ9v/Mx3Id9RpXgBWc8kj7HY\nwLWbmxuFCxfmzp073L59O+3Lzc3N6gVCiNyuenXYuRP+7/+gaVP48MP8v7SHs70zXz7/JS/Xfhm/\nJX7sitmldySRg57Ykhg9ejQrV66kevXq2Dw0KidLhQvx7y5ehH794N49rVVREOZ7/PTrT/T6phfv\nNnuXwfUHy6qyuYjFupvc3d05deqUrjfQPUyKhMhLlILFi7X1oP7aCc/eXu9UlvXrH7/SaXUnGlRo\nwPzg+TjayTI+uYHFupt8fX25e/dulkIJUdAZDNry41FRsHu3tmDgsWN6p7KsaiWqEdk3kvgH8QR8\nGcC1e9f0jiSy4YktiUOHDtGpUye8vLzSFvYzGAxs2LDBKgH/SVoSIq9SCr74AkaPhsGDtVlQuaSB\nbhFKKabunspnhz9jfff1NHRtqHekAs1i3U21atVi0KBBeHl5pY1JGAwGmjdvnrWk2SRFQuR1V67A\ngAFw+TIsWwb5/bajH878QN8NfZnRagZ9jH30jlNgWaxI+Pn5sX///iwHy2lSJER+oBR89ZW2umy/\nfvDee5CfV+A/dfMUnVZ3om31tnzU5iPsbfP5wEwuZLEiMWrUKJydnWnfvn26fST0uutaioTIT65f\nh0GD4OxZrVXRoIHeiSznTtIdeq7vSVJqEmu6raF0odJ6RypQLFYkAgICHjuNTabACpEzlILQUG32\n00svwaRJoNMiyxZnMpsYv2M8q0+u5ruQ76hdrrbekQoMi+4nkZtIkRD51Y0bMHQoHD+u3VfRuLHe\niSwn9EQoQ38cyrx28+ju2V3vOAWCxabAXrlyhV69etG6dWsAzpw5w6JFi54+oRDiX5UtC2vWwNSp\n0KULjBwJCQl6p7KMEK8QtvXexuifRjN2+1hMZpPekUQGnlgkevXqRYcOHfj9998B7ea6OXPmWDyY\nEAVVly7w889ay8LHR9s2NT/yLefLwX4HiYyNpOPqjsQnxesdSTxGhkUi9X8LzsTFxRESEoLt/5a0\ntLOzw87uidtQCCGyoXRpbfbTzJnw4oswbBjcv693qpxXpnAZtvbainsJdxp83oDTt07rHUn8Q4ZF\nosH/plkULlyYW7dupT0eHR2dbpZTRpKSkqhfvz5Go5EaNWowcuRIAPbu3Yuvry9eXl7Url2bffv2\npb1m+vTpeHh44O3tzdatW7P8RwmRX3TsCCdOaOs/+fjAjh16J8p59rb2zGk7h9FNRtNsWTM2nt34\n5BcJ61EZ8PX1VUoptW/fPlW3bl1VrFgx1bRpU1WlShV18ODBjF6WTkJCglJKqZSUFNWwYUO1Y8cO\n5e/vrzZv3qyUUmrTpk3K399fKaXU4cOHVb169VRqaqqKjY1Vbm5u6sGDB48c818iC5GvhYUpVamS\nUgMGKBUfr3cay4i8HKkqflxRTdk1RZnNZr3j5CtZfe/MsN/o5s2bzJw5E6UUISEh2NjYoJTCbDaz\ne/du6tev/8QC5Py/eXzJycmYTCbKli2Lq6sr8fFa3+OdO3eoUkVbez4sLIwePXpga2tLxYoV8fT0\n5ODBg/j7+2e/EgqRD7Rrp41VvPkmeHvDokUQFKR3qpzl5+rHwdcO8kLoCxz9/SjLOi2jiEMRvWMV\naBl2N5lMJu7du8f9+/dJSEjg/v37/PnnnyQmJnLv3r1MHdxsNuPr64uLiwuBgYF4enrywQcf8MYb\nb1C5cmXeeustpk+fDmizqFxdXdNe6+rqSmxsbDb/PCHyl2ee0VaVXbxYW9qjb1+4c0fvVDmrQtEK\nhL8STlGHojRe0piLf1zUO1KBlmFLoly5ckyYMCFbB7exseHo0aPEx8cTFBREeHg4U6ZMYc6cOXTu\n3Jm1a9fy6quvsm3btqc67sSJE9O+DwgIICAgIFs5hchr2rTRWhWjR2utis8+g+BgvVPlHCc7J5Z0\nXMKnBz+l0ZJGfPXCV7Ss1lLvWHlKeHg44eHh2T5OhjfTGY1GoqOjs32Cv0yePBl7e3umTJnC/f9N\n01BKUbRoUe7fv8/kyZNxdnbmzTffBKB9+/a88847NGnSJH1guZlOiHR27tRaFP7+8MknULKk3oly\n1s6LO3lx/YuM8R/DiIYjZCOjLMrxm+l++umnbAWKi4tL65ZKTExk27ZteHl5UaVKFXbt0rY33LFj\nB1WrVgWgXbt2hIaGkpqaSmxsLCdOnEibYSWEyFhgoHaXdvHiWqviu+/0TpSzAqsGsr/ffr44+gV9\nvu9DUmqS3pEKlAy7m0qVKpWtA1+9epWXXnoJpRRJSUn07NmT9u3bU7JkSQYPHkxKSgqOjo4sWbIE\ngLp169K5c2d8fHywsbFh4cKF2Of3LbyEyCFFisCcOdCtG7z6qrYW1Ny52v0W+YFbcTf2vrqXVze8\nSrNlzfg25FsqFquod6wCQdZuEiKfSUiAd9+Fr7/+u3DkF0opZuydwdyDc1nbbS2NK+XjBa5ymCzw\nJ4RIJzJSa1V4ecG8edraUPnFpnObeOW7V5jaYiqv1X1N7zh5gsUW+BNC5E2NGkF0NLi7a3drr1ql\nLUueH7R7th27++xm5v6ZDAkbQrIpWe9I+Za0JIQoAA4dgj59oHp1WLAAypfXO1HOiE+Kp9e3vYhP\nimdd93WULZyPmks5TFoSQogM1a8PUVHa7KfatWH58vzRqnjG6Rm+7/E9zao0o/7i+hy5dkTvSPmO\ntCSEKGCio7VWRcWKsHAhPLTQQZ627pd1DAobxOz/zKand0+94+Q60pIQQmSK0QgHD0LDhtr3S5bk\nj1ZFV4+ubH9pO+N3jOetrW/JRkY5RFoSQhRgx49rrYrSpbX1oCpX1jtR9sUlxNF9XXfsbOxY3WU1\nJZxL6B0pV5CWhBDiqfn4wIEDEBAAdetqa0CZzRAWFkFQ0HgCAiYSFDSesLC8sz1eqUKl2NJrCx6l\nPai/uD7zD83nTlL6VRDvJN0h7GyYTgnzFmlJCCEA+OUXrVWRmBhBfPwWLl2amvY7d/dxzJ4dRHBw\nMx0TPr3lx5YzcstIGlRswKouqyjuVJw7SXcYt30cU1tOpbhTcb0jWo3cTCeEyLbUVPD0HM/Zs1Me\n+V1Q0Lts3jxZh1TZc/DKQTqHdqZC0QqEdg3l430fF7gCAdLdJITIAXZ2UL7845d0S0qytXKanNGg\nYgOi+kehlMJ9jjv96/YvcAUiO6RICCHScXRMfezj586ZOHzYymFyiJOdE/Ur1KePbx+afdGMiJi8\nM8aiNykSQoh0hg9vg7v7uHSPubmNpU2b1nTtqi338fXXkJxHVsL4awxieqvpLO20lJltZhL0VRDz\nDs7TO1qeIGMSQohHhIVFMHfuNpKSbHFyMjFsWGuCg5thMsEPP2jLkJ86Bf37a9uo5uZlPsLOhtGk\ncpN0XUyRlyPptrYb7Z5tx5y2c3Cyc9IxoXXIwLUQwqpOnoRPP4XVq6FtWxg2DPz8IK9sHHf3wV36\nbujLxT8usq77OtyKu+kdyaJk4FoIYVWentpigRcvamtD9eql/ffLLyEpD2weV8yxGGu6rqGnd08a\nft6Qzec36x0pV5KWhBAiR5jN8OOPWldUdDT06weDBuWNtaF2/7abHut70L9Of95t/i42hvz3+Vm6\nm4QQucaZM1pX1FdfQcuWMHw4+Pvn7q6oa/euEbIuhMIOhVnZeSWlCmVvC+fcRrqbhBC5Rs2aWosi\nJgaaNdNaFX8tJpiYqHe6xytftDzbX9qOZxlP6i2uR9TVKL0j5QrSkhBCWJzZDNu2aYXjwAFtW9XB\ng6FKFb2TPd5fy45PazGNfnX6YcjNTaBMku4mIUSecOGCtuf2l19qrYxhwyAwMPd1RZ2+dZoXQl/A\nz9WPee3m4WzvrHekbJEiIYTIU+7fh5UrtdaFwQBDh0Lv3lC4sN7J/nY/+T79NvTjbNxZ1nVfR7US\n1fSOlGUyJiGEyFOKFIGBA+HECZgzB7Zs0fazGDVKa23kBkUcirCqyype8X2FRksasfHsRr0jWZ20\nJIQQuUZMjHbvxdKl2s55w4ZB69Zgkws+zu69tJeQdSH08e3DxICJ2NrkrQUPpbtJCJFvJCTAqlVa\nV1RiotYV9fLLUKyYvrl+v/87Pdb3wN7Gnq+7fE3pQqX1DfQUpLtJCJFvFCoEfftqN+V9/jns3g1u\nblrL4swZ/XK5FHFhW+9t1Clfh7qL6nLwykH9wliJFAkhRK5lMEDTprBmjbYf9zPPaDOigoJg40Zt\naq212dnY8UGrD5j9n9m0/7o9Cw4tyNe9G9LdJITIU5KSIDRU64q6cweGDNG2XS2uwz5C5+LO8cKa\nFzCWM/JZ+88oZF/I+iEyKVd2NyUlJVG/fn2MRiM1atRg5MiRAISEhGA0GjEajVStWhWj0QhATEwM\nzs7Oab8bPHiwJeMJIfIgJydtfOLQIVixQvtv1araOlEnT1o3y7OlnmV/3/0oFI2WNOL87fPWDWAF\nj9+nMIc4OTkRERGBs7Mzqamp+Pv7s3PnTkJDQ9Oe8+abb1L8oY8A1atXJzo62pKxhBD5gMGgbYDU\nqBFcuwYLF0KrVuDhoY1ddOgAtlaYgFTYoTDLn1/OgsMLaLykMYs7LKbTc50sf2IrsfiYhLOzdpdi\ncnIyJpMJFxeXtN8ppVizZg0vvviipWMIIfKx8uVh4kT47TdtwHvGDHB3hw8/hLg4y5/fYDAwuP5g\nNry4gWE/DuOdn94h1fz4bWDzGosXCbPZjK+vLy4uLgQGBuLh4ZH2u927d+Pi4oK7u3vaYzExMfj6\n+tK4cWN27Nhh6XhCiHzEwQF69oTISFi3Tut+ql5dW2Dw2DHLn9/P1Y+o/lEcvnaYoJVB3PjzhuVP\namEWLxI2NjYcPXqU2NhYIiIiCA8PT/vdqlWr6NmzZ9rPFSpU4MqVKxw9epR58+bRu3dv7ty5Y+mI\nQoh8qF49bX2oM2e0MYvgYG1m1Nq1kJJiufOWKVyGzf+3mUaujai7qC6RlyMtdzIrsOrspsmTJ2Nv\nb8+YMWNITU3F1dWVI0eOUKFChcc+PygoiEmTJuHn5/d3YIOBCRMmpP0cEBBAQECApaMLIfK4lBT4\n7jttVtTFi9qSIP37Q5kyljvnD2d+oO+Gvrzb7F2GNhhq1dVkw8PD030onzRpUtZmhioLunXrlrp7\n965SSqmEhATVtGlTtXHjRqWUUj/++KMKCAhI9/y4uDhlMpmUUkpdvHhRVahQQd28eTPdcywcWQhR\nAERHK9W3r1LFiyv10ktKHTpkuXOdjzuvai+orV5c96K6/+C+5U70BFl977Rod9PVq1dp1qwZvr6+\nGI1GWrVqRXBwMAChoaGPDFjv3LkTHx8ffHx86NChA3PmzKF06bxz27sQIm/w9dXu5D5/Xturu2tX\nbZbU119DcnLOnsu9pDuRfSNxtHOk4ecNORt3NmdPYGFyM50QosAzmeCHH7TVaE+fhgEDtK9y5XLu\nHEopFh9ZzPgd4/ms/We8UOuFnDt4JsgCf0IIkQNOnND25w4NhXbttHsuGjbMuU2RDl05RLe13ejm\n0Y3praZjZ2PR29XSSJEQQogc9McfsGyZtoteyZJasQgJAUfH7B87LiGO//vm/0hMTSS0ayjliuRg\nkyUDUiSEEMICTCb48UdtVtTRo/Daa9rMKFfXbB7XbOL9Xe+zJHoJq7uuxr+yf84EzkCuXLtJCCHy\nOltbaN9e2zkvIgLi48HHB7p315Ywz+pnVlsbWyYFTmJRh0V0WdOFWZGzcuUHYGlJCCHEU7p7V7tR\n79NPwdlZ64rq2VP7Pisu/nGRrmu7Ur1kdT7v8DlFHYvmbGCkJSGEEFZTrJhWGE6d0taJ+vZbbX/u\n0aO19aOeVtUSVdn76l6KORSjwecNOHXzVM6HziIpEkIIkUU2Nn9vgBQZqd3VXacOdO4MO3Y8XVeU\nk50Tizsu5q3Gb9Hsi2asObnGcsGfgnQ3CSFEDrp/H1au1Aa6DQZtf+7evaFw4cwf48i1I3Rd05VO\nNTvxYesPsbe1z3Yumd0khBC5iFKwc6dWLCIitI2ShgzRljDPjNuJt+n9bW/ik+JZ020NFYo+fo27\nzJIxCSGEyEUMBmjRQhuviIoCOzvw89M2Q9q69cn7c5d0LskPL/5AkHsQ9RbVY1fMLusE/wdpSQgh\nhJUkJGjrQ82dCw8eaF1RL78MRZ8wmWnrha289O1LvNn4Td5o9EaWVpOV7iYhhMgjlNLusZg7F7Zv\nh169tIJRo0bGr/ntzm90W9uNSs9UYlmnZRRzLPZU55TuJiGEyCMMhr83QDp2TGtJNG0K//kPhIU9\nviuqSvEq7O6zm7KFylJ/cX1O3jhpnazSkhBCCP0lJWmLCs6dC3fuaIPcffpA8eKPPnf5seW8sfUN\n5vxnDi96v/joEx5DupuEECIfUAr279eKxY8/Qo8e2o17Hh7pn3fs+jG6rOlC2+pt+TjoYxxsHf71\nuNLdJIQQ+YDB8PcGSL/8Ai4u0LKl9vXdd9qCgwC1y9XmcP/DXLp7iYAvAoi9G2uZPNKSEEKI3C05\nGdat01oX167B4MHQr5+2hLlZmZmxZwZzDs7hqxe+okXVFo89hnQ3CSFEAXD4sFYsNmyALl20rqja\ntWH7r9vp9W0vRjQcwdtN3sbGkL6jSIqEEEIUIDduwOLFsGABVKsGw4dDvRaxvPhtN8oWLsuXz39J\ncae/R72lSAghRAGUkqKNVcydCxcvwmsDk7lU6w12XdnMiIYjKHOtKkvnR7J161QpEkIIUZAdPart\ncbF+PXj3/IqosoNRV0uSuDwakkpIkRBCCAFxcbBkCbw7tz/JnXdAqhMsOClTYIUQQkCpUvD22+BX\nrQIsOgJ3s74htxQJIYTIp5ycUsFghj+qZfkYUiSEECKfenVwI4p1bgk7pmX5GFIkhBAinypSCxaF\nvE9Q84+zfAwZuBZCiAJA1m4SQgiR4yxWJJKSkqhfvz5Go5EaNWowcuRIAEJCQjAajRiNRqpWrYrR\naEx7zfTp0/Hw8MDb25utW7daKpoQQohMsrPUgZ2cnIiIiMDZ2ZnU1FT8/f3ZuXMnoaGhac958803\nKf6/xdKjoqL45ptv+Pnnn7l+/Tr+/v6cOXMGB4d/X/62IAsPDycgIEDvGLmCXIu/ybX4m1yL7LNo\nd5OzszMAycnJmEwmXFxc0n6nlGLNmjW8+KK2YUZYWBg9evTA1taWihUr4unpycGDBy0ZL88LDw/X\nO0KuIdfib3It/ibXIvssWiTMZjO+vr64uLgQGBiIx0O7ZuzevRsXFxfc3d0BuHLlCq6uf9/w4erq\nSmysZdZHF0IIkTkWLRI2NjYcPXqU2NhYIiIi0lX1VatW0bNnT0ueXgghRHYpK3n//ffV9OnTlVJK\npaSkKBcXF3XlypV0v//vf/+b9nNwcLDas2fPI8dxd3dXgHzJl3zJl3w9xZe7u3uW3rstNnAdFxeH\ng4MDRYsWJTExkW3btjF69GgAfvrpJ2rVqkWFChXSnt+uXTsGDhzI66+/zvXr1zlx4gQNGjR45Ljn\nz5+3VGQhhBD/YLEicfXqVV566SWUUiQlJdGzZ0+Cg4MBCA0NTRuw/kvdunXp3LkzPj4+2NjYsHDh\nQuzt7S0VTwghRCbkuTuuhRBCWE+uveN68+bNeHt74+HhwYwZMx77nOHDh+Pp6UmdOnWIjo62ckLr\neXPkaAMAAAoKSURBVNK1WLFiBT4+Pnh7e1OvXj2ioqJ0SGkdmfl3AXDo0CHs7Oz45ptvrJjOujJz\nLcLDw2nQoAG+vr40b97cygmt50nX4vr167Rs2RJPT09q1qzJwoULdUhpea+++iouLi54e3tn+Jyn\nft/M0kiGhSUlJSk3NzcVGxurUlJSVL169dSRI0fSPWfdunWqU6dOSimljhw5omrXrq1HVIvLzLU4\ncOCAunv3rlJKqR9//FH5+vrqEdXiMnMtlFIqNTVVBQYGquDgYLVu3TodklpeZq7FtWvXlKenp/r9\n99+VUkrFxcXpEdXiMnMtxo0bp8aMGaOUUurmzZuqePHiKikpSY+4FhUREaGOHDmivLy8Hvv7rLxv\n5sqWxIEDB/D09KRixYrY2dkREhJCWFhYuuds2rSJ3r17A2A0GklNTc2X91Vk5lo0aNCAokWLAtCk\nSROuXLmiR1SLy8y1AJg7dy5du3alTJkyOqS0jsxci9WrVxMSEkLZsmUBKFmypB5RLS4z16JSpUrc\nvXsXgLt371KmTBkcHR31iGtRTZs2pUSJEhn+Pivvm7mySMTGxlKpUqW0nx93Y11mnpMfPO3fuXDh\nQjp16mSNaFaXmWtx5coVvv/+ewYNGgRoK1/mR5m5FmfOnOHq1as0atQIHx8fPv/8c2vHtIrMXIvX\nXnuNkydPUqFCBWrXrs3s2bOtHTNXyMr7psVmN2VHZv+Prf4x5p4f3xCe5m8KDw9n6dKl7N2714KJ\n9JOZa/H666/zwQcfpC2L/M9/I/lFZq6FyWTixIkT7Nixg4SEBPz8/GjUqBGenp5WSGg9mbkW06ZN\nw9fXl/DwcC5cuEDr1q05duxYWgu8IHna981c2ZJwdXXl8uXLaT9fvnw5XfV73HNiY2PTLeuRX2Tm\nWgAcP36cfv36sWHDhn9tbuZlmbkWUVFR9OjRg6pVq7J+/XoGDx7Mhg0brB3V4jJzLSpXrkybNm1w\ndnamVKlSNG/enOPHj1s7qsVl5lrs2bOHbt26AeDu7k7VqlU5deqUVXPmBll638yxEZMclJiYqKpU\nqaJiY2NVcnKyqlevnoqKikr3nHXr1qnnn39eKaVUVFSU8vHx0SOqxWXmWvz222/K3d1dRUZG6pTS\nOjJzLR72yiuvqPXr11sxofVk5locOXJEtWzZUqWmpqo///xTeXh4qOjoaJ0SW05mrsXgwYPVxIkT\nlVJKXb9+XZUrVy5tQD+/uXjx4r8OXD/t+2au7G5ycnJiwYIFBAUFYTab6d27N3Xq1EmbtjZgwAC6\ndOnCzp078fT0xNHRkWXLlumc2jL+v737C2nqDeMA/i3pJlcLzEr7c1MIntx2VqFMtzWq5TCLjFUT\nhEosupjLwouMCtPUi+qiSDCCTKOM7GLRRYKZnloIXRjZuoiKRhQuWkkYNFn6/C6G5+ecZ2mFv/Xb\n87k67znvOe/7novz7JyXPe9U7kVNTQ0GBwfl7/Bz5sz5X2bQncq9SBRTuRd6vR42mw1arRahUAhl\nZWUQRfE/7vmfN5V7cfLkSZSUlEAQBIyMjOD06dPyhP7/SXFxMSRJQiAQwPLly3Hq1CmEQiEAv/7c\n5D/TMcYYUxSXcxKMMcbiAwcJxhhjijhIMMYYU8RBgjHGmCIOEowxxhRxkGCMMaaIgwSLG7Nnz5aT\njwHAjx8/kJqaiq1bt8Y87+rVqygvL59WW7t27UJWVtYfyeFTX18fUc7Ly/vtazIWLzhIsLiRnJyM\nFy9eIBgMAgA6OzuxbNmyn+aWmW7OLr/fj6dPn8Lr9eLQoUMRx0ZHR6fXaQANDQ0R5XjOnfUr42OJ\njYMEiysFBQVymue2tjYUFxfLCckCgQDy8/Oh0Wiwdu1a9PX1RZ3v9/tRWFgInU4HURQhSVJUnc2b\nN+PDhw/Q6/XweDywWCw4fPgwDAYDzp8/j7t37yInJwcajQZmsxkDAwMAgKGhITgcDqxevRo6nQ63\nb99GVVUVvn//Dr1eL78FqVQqAOEHcnl5OQRBgCAIaG1tBRBOxGixWOBwOJCRkYGdO3f+NBHh9u3b\nce3aNQDhTL8lJSVRdd68eYPc3FzodDoYjUb4fD4AwN69e3Hw4EHk5eXh6NGjEeesX78ez549k8tG\noxHPnz+P2ReWYP5YwhDGfpNKpaL+/n6y2+0UDAZJFEXq6emhwsJCIiLav38/1dfXExGRJEmUmZlJ\nRETNzc3kdDqJiKioqIg8Hg8R/ZvTaiKfzxeR28ZisZDL5ZLLX79+lbcvX74sX9vlclFlZWVUPZVK\nFTUOIqLr169Tfn4+EYUX/ElPT6f3799Td3c3qdVq8vv9NDo6SgaDgbq7u2Pem48fP9KqVavo4cOH\nlJGRQYODg1F1rFYr3bhxg4iIWlpayGazERHRnj175Hw9E7W0tFBFRQUREb18+ZLWrVsXsx8s8cRl\n7iaWuDQaDXw+H9ra2rBly5aIY48fP8axY8cAAGazGd++fUMgEIioc//+fbx9+1YuDw8PY2hoKCIl\nNE3yq91ut8vbr1+/xpEjR/D582eEQiGsWLECANDV1YU7d+7I9ebPnx9zLB6PBw6HA0B4wZ+NGzei\nt7cXqampyM7OxuLFiwEAoihGZOaczKJFi1BTU4MNGzbA7XZjwYIFUXV6e3tx7949AOEcPk6nE0D4\nc9yOHTsmva7dbkdtbS3OnDmDK1euYN++fTH7wRIPBwkWd7Zt24bKykpIkoRPnz5FHJv4gJ84HzFr\n1ix5fevpSE5OlredTieOHz+OgoICSJKE6upqxfZjGVvTYrL+jl8VLSkpaUpzBf39/Vi4cKHiyoOx\n5mbmzp2ruN9qtcLtdqO9vX3ST3gssfGcBIs7paWlqK6ujlocx2Qy4ebNmwCAR48eYd68eUhJSYmo\ns2nTJjQ1Ncllr9c7pTbHP8yDwSCWLFkCAPI8AgBYrVY5sygAeTnMpKQkjIyMRF3TZDKhvb0dRIQv\nX77gwYMHMBgMMQNNVVUV3G531P4nT56go6MDfX19OHv2rDzfMF5ubi5u3boFILx0qclk+smow8rK\nyuByuZCdnQ21Wj2lc1ji4CDB4sbYL+GlS5dGfCoZ219XV4eenh5otVpUVFTIE7nj6zQ1NaGzsxMa\njQZZWVm4cOFCzLYmK584cQJFRUXIyclBSkqKfKy2thbv3r2DIAgQRRFdXV0AwhPDmZmZ8sT1WP3d\nu3dj5cqVEAQBRqMRDQ0NSE9Pj+jvxPa9Xi/S0tIijg0PD+PAgQNobm5GWloazp07h9LS0qgxNTY2\n4uLFi9Bqtbh06RIaGxsVxzvemjVroFar+VMTmxSnCmcsjthsNnR0dMxomwMDAzCbzXj16tWMtsv+\nDvwmwVgcmekA0draCqPRiLq6uhltl/09+E2CMcaYIn6TYIwxpoiDBGOMMUUcJBhjjCniIMEYY0wR\nBwnGGGOKOEgwxhhT9A+y/HS4V4Zf1wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x31cbbd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pKeDxeOjTpw88PDw0EZsMXUrSTglJCVgXvQ4lTAlMeaYY6TsSm55ugsU7Ftg0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\niJz/A9vzOGCUmCVhAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3e71b10>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.6 page no : 158"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "# variables\n",
      "p = 100                   # pressure Kpa\n",
      "# from table\n",
      "n_heptaneA = 13.8587\n",
      "n_hexaneA = 13.8216\n",
      "n_heptaneB = 2911.32\n",
      "n_hexaneB = 2697.55\n",
      "n_heptaneC = 56.51\n",
      "n_hexaneC = 48.78\n",
      "xA = .25\n",
      "\n",
      "# Calculations and Results\n",
      "\n",
      "# for T = 360   Initial guess\n",
      "T1 = 360\n",
      "lnPaS = n_hexaneA - (n_hexaneB/(T1- n_hexaneC))\n",
      "PaS = round(math.e**lnPaS,2)\n",
      "lnPbS = n_heptaneA - (n_heptaneB/(T1- n_heptaneC))\n",
      "PbS = round(math.e**lnPbS,2)\n",
      "P = xA*PaS + (1 - xA)*PbS\n",
      "\n",
      "print \"P = %.1f kPa\" %P\n",
      "\n",
      "# Since total pressure < 100 Kpa, equilibrium temperature is not equal to 360K.\n",
      "# for T = 365 - Assume\n",
      "T1 = 365\n",
      "lnPaS = n_hexaneA - (n_hexaneB/(T1- n_hexaneC))\n",
      "PaS = round(math.e**lnPaS,2)\n",
      "lnPbS = n_heptaneA - (n_heptaneB/(T1- n_heptaneC))\n",
      "PbS = round(math.e**lnPbS,2)\n",
      "P = xA*PaS + (1 - xA)*PbS\n",
      "\n",
      "print \"P = %.2f kPa\"%P\n",
      "\n",
      "# As the pressure > 100 kPa, the temperature lies between 360 and 365 K.\n",
      "# for T = 361.125 -- assumption\n",
      "T1 = 361.125\n",
      "lnPaS = n_hexaneA - (n_hexaneB/(T1- n_hexaneC))\n",
      "PaS = round(math.e**lnPaS,2)\n",
      "lnPbS = n_heptaneA - (n_heptaneB/(T1- n_heptaneC))\n",
      "PbS = round(math.e**lnPbS,2)\n",
      "P = xA*PaS + (1 - xA)*PbS\n",
      "\n",
      "print \"P = %.f kPa\"%P\n",
      "print \"Therefore, the bubble point temperature = %.3f K\"%T1   # last assumed for T1\n",
      "\n",
      "\n",
      "# Part b\n",
      "Pa = xA*PaS\n",
      "Ya = Pa/P\n",
      "\n",
      "print \"Partial pressure of n-Hexane in vapour at the bubble point is = %.2f kPa\"%Pa\n",
      "print \"Mole fraction of hexane in the vapour is Ya = %.4f\"%Ya\n",
      "print \"The vapour contains %.2f %% hexane and %.2f %% heptane.\"%(Ya*100,(1-Ya)*100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P = 96.7 kPa\n",
        "P = 112.04 kPa\n",
        "P = 100 kPa\n",
        "Therefore, the bubble point temperature = 361.125 K\n",
        "Partial pressure of n-Hexane in vapour at the bubble point is = 44.65 kPa\n",
        "Mole fraction of hexane in the vapour is Ya = 0.4465\n",
        "The vapour contains 44.65 % hexane and 55.35 % heptane.\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.7 page no : 159"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables \n",
      "#lnPas = 14.5463 - 2940.46/(T - 35.93)\n",
      "#lnPbs = 14.2724 - 2945.47 / (T - 49.15)\n",
      "#xa = (P - Pbs)/(Pas - Pbs)\n",
      "#Ya = Pas * (P - Pbs)/(P * (Pas - Pbs))\n",
      "Ya = 0.4                            # vapour phase\n",
      "P = 65.                             #kPa\n",
      "#various temperature value are assumed and tried till LHS = RHS, we get\n",
      "T = 334.15                          #K\n",
      "\n",
      "# Calculation \n",
      "Pas = math.exp(14.5463 - 2940.46/(T - 35.93)) \n",
      "Pbs = math.exp(14.2724 - 2945.47 / (T - 49.15)) \n",
      "xa = (P - Pbs)/(Pas - Pbs) \n",
      "\n",
      "# Result \n",
      "print \"(a)The Dew point temperature at 65 kPa = \",T,\"K\"\n",
      "print \"    Concentration of the first drop of liquid = %.2f\"%xa\n",
      "T1 = 327.                           #K\n",
      "Pas1 = math.exp(14.5463 - 2940.46/(T1 - 35.93)) \n",
      "Pbs1 = math.exp(14.2724 - 2945.47 / (T1 - 49.15)) \n",
      "xa1 = Ya * Pbs1 / (Pas1 - Ya*(Pas1 - Pbs1)) \n",
      "P1 = xa1 * Pas1 / Ya \n",
      "print \"(b)The dew point pressure at 327 K = %.2f kPa\"%P1\n",
      "print \"    Concentration at 327K = %.4f\"%xa1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)The Dew point temperature at 65 kPa =  334.15 K\n",
        "    Concentration of the first drop of liquid = 0.24\n",
        "(b)The dew point pressure at 327 K = 50.09 kPa\n",
        "    Concentration at 327K = 0.2354\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.8 pageno : 163"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "MW = 44.032                # mole fraction of acetaldehyde\n",
      "Mwater = 18.016            \n",
      "x = 2.                      #%    acetaldehyde weight\n",
      "Pa = 41.4                   #kPa   solution\n",
      "\n",
      "# Calculation \n",
      "Mfr = (x/MW)/(x/MW + (100-x)/Mwater) \n",
      "#henry's law gives Pa = Ha * xa\n",
      "Ha = Pa / Mfr \n",
      "Molality = 0.1 \n",
      "Mfr1 = Molality / (1000/Mwater + Molality) \n",
      "Pa1 = Ha * Mfr1 \n",
      "\n",
      "# Result\n",
      "print \"Partial Pressure = %.f kPa\"%Pa1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Partial Pressure = 9 kPa\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.9 pageno : 177"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables \n",
      "#1 - pentane, 2 - hexane, 3 - heptane\n",
      "\n",
      "x1 = 0.6 \n",
      "x2 = 0.25 \n",
      "x3 = 0.15 \n",
      "A1 = 13.8183 \n",
      "A2 = 13.8216 \n",
      "A3 = 13.8587 \n",
      "B1 = 2477.07 \n",
      "B2 = 2697.55 \n",
      "B3 = 2911.32 \n",
      "C1 = 39.94 \n",
      "C2 = 48.78 \n",
      "C3 = 56.51 \n",
      "#As raoults law is applicable, Ki = yi/xi = Pis/P\n",
      "#yi = xi*Pis/P\n",
      "#ln P = A- B/(T-C)\n",
      "#Assuming,\n",
      "P = 400.                #kPa\n",
      "T = 369.75              #K\n",
      "\n",
      "# Calculation \n",
      "Pas1 = math.exp(A1 - B1 / (T - C1)) \n",
      "Pas2 = math.exp(A2 - B2 / (T - C2)) \n",
      "Pas3 = math.exp(A3 - B3 / (T - C3)) \n",
      "Yi = (x1*Pas1 + x2*Pas2 + x3*Pas3)/P \n",
      "print \"(a)bubble point temperature of the mixture = \",T,\"K\"\n",
      "y1 = x1*Pas1/P \n",
      "y2 = x2*Pas2/P \n",
      "y3 = x3*Pas3/P \n",
      "\n",
      "# Result \n",
      "print \"(b)composition of n-pentane in vapour = %.2f %%\"%(y1*100)\n",
      "print \"composition of n-hexane in vapour = %.2f %%\"%(y2*100)\n",
      "print \"composition of n-heptane in vapour = %.2f %%\"%(y3*100)\n",
      "T1 = 300.               #K\n",
      "Ps1 = math.exp(A1 - B1 / (T1 - C1)) \n",
      "Ps2 = math.exp(A2 - B2 / (T1 - C2)) \n",
      "Ps3 = math.exp(A3 - B3 / (T1 - C3)) \n",
      "P1 = x1*Ps1 + x2*Ps2 + x3*Ps3 \n",
      "print \"(c)Bubble point pressure = %.1f kPa\"%P1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)bubble point temperature of the mixture =  369.75 K\n",
        "(b)composition of n-pentane in vapour = 82.32 %\n",
        "composition of n-hexane in vapour = 14.08 %\n",
        "composition of n-heptane in vapour = 3.60 %\n",
        "(c)Bubble point pressure = 50.4 kPa\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.10 pageno : 178"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables \n",
      "#1 - pentane, 2 - hexane, 3 - heptane\n",
      " \n",
      "y1 = 0.6 \n",
      "y2 = 0.25 \n",
      "y3 = 0.15 \n",
      "A1 = 13.8183 \n",
      "A2 = 13.8216 \n",
      "A3 = 13.8587 \n",
      "B1 = 2477.07 \n",
      "B2 = 2697.55 \n",
      "B3 = 2911.32 \n",
      "C1 = 39.94 \n",
      "C2 = 48.78 \n",
      "C3 = 56.51 \n",
      "P = 400.                    #kPa\n",
      "T = 300.                    #K\n",
      "#As raoults law is applicable, Ki = yi/xi = Pis/P\n",
      "#xi = yi*P/Pis\n",
      "#ln P = A- B/(T-C)\n",
      "#Assuming,\n",
      "T1 = 385.94                 #K\n",
      "\n",
      "# Calculation \n",
      "Pas1 = math.exp(A1 - B1 / (T1 - C1)) \n",
      "Pas2 = math.exp(A2 - B2 / (T1 - C2)) \n",
      "Pas3 = math.exp(A3 - B3 / (T1 - C3)) \n",
      "\n",
      "# Result\n",
      "print \"(a)Dew point temperature of the mixture = \",T1,\"K\"\n",
      "Ps1 = math.exp(A1 - B1 / (T - C1)) \n",
      "Ps2 = math.exp(A2 - B2 / (T - C2)) \n",
      "Ps3 = math.exp(A3 - B3 / (T - C3)) \n",
      "P1 = 1/(y1/Ps1 + y2/Ps2 + y3/Ps3) \n",
      "print \"(b)Dew point pressure = %.2f kPa\"%P1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Dew point temperature of the mixture =  385.94 K\n",
        "(b)Dew point pressure = 23.79 kPa\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.11 page no :180"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "#1 - methanol, 2 - ethanol, 3 - propanol\n",
      "x1 = 0.45 \n",
      "x2 = 0.3 \n",
      "x3 = 1 - (x1 + x2) \n",
      "P = 101.3                   #kPa\n",
      "# by drawing the temperature vs vapour pressure graph and interpolation,assuming,\n",
      "T = 344.6                   #K\n",
      "Ps1 = 137.3 \n",
      "Ps2 = 76.2 \n",
      "Ps3 = 65.4 \n",
      "\n",
      "# Calculation \n",
      "y1 = x1 * Ps1 / P \n",
      "y2 = x2 * Ps2 / P \n",
      "y3 = x3 * Ps3 / P \n",
      "\n",
      "# Result\n",
      "print \"(a)Bubble point temperature = \",T,\"K\"\n",
      "print \"Composition of methanol in vapour = %.f %%\"%(y1*100)\n",
      "print \"Composition of ethanol in vapour = %.1f%%\"%(y2*100)\n",
      "print \"Composition of propanol in vapour = %.1f%%\"%(y3*100)\n",
      "#again, for xi = 1\n",
      "T1 = 347.5                  #K\n",
      "P1 = 153.28 \n",
      "P2 = 85.25 \n",
      "P3 = 73.31 \n",
      "xa = x1 * P / P1 \n",
      "xb = x2 * P / P2 \n",
      "xc = x3 * P / P3 \n",
      "print \"(b)Dew point temperature = \",T1,\"K\"\n",
      "print \"Composition of methanol in liquid = %.1f %%\"%(xa*100)\n",
      "print \"Composition of ethanol in liquid = %.1f %%\"%(xb*100)\n",
      "print \"Composition of propanol in liquid = %.1f %%\"%(xc*100)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)Bubble point temperature =  344.6 K\n",
        "Composition of methanol in vapour = 61 %\n",
        "Composition of ethanol in vapour = 22.6%\n",
        "Composition of propanol in vapour = 16.1%\n",
        "(b)Dew point temperature =  347.5 K\n",
        "Composition of methanol in liquid = 29.7 %\n",
        "Composition of ethanol in liquid = 35.6 %\n",
        "Composition of propanol in liquid = 34.5 %\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.12 pageno : 181"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "xp = 0.25                           # propane\n",
      "xnb = 0.4                           # n-butane\n",
      "xnp = 0.35                          # n-pentane\n",
      "P = 1447.14                         #kPa  \n",
      "#assuming temperatures 355.4 K and 366.5 K , corresponding Ki \n",
      "# values are found from nomograph and total Ki value are 0.928 and 1.075 resp, thus bubble point temperature lies between, using interpolation bubble point temperature is found to be,\n",
      "Tb = 361.                           #K\n",
      "print \"(a) The buuble point temperature = \",Tb,\"K\"\n",
      "\n",
      "\n",
      "# Calculation \n",
      "#At 361,\n",
      "Kip = 2.12 \n",
      "Kinb = 0.85 \n",
      "Kinp = 0.37 \n",
      "xp1 = Kip * xp \n",
      "xnb1 = Kinb * xnb \n",
      "xnp1 = Kinp * xnp \n",
      "\n",
      "# Result\n",
      "print \"concentration of propane at bubble point = \",xp1\n",
      "print \"concentration of n-butane at bubble point = \",xnb1\n",
      "print \"concentration of n-pentane at bubble point = %.3f\"%xnp1\n",
      "#At dew point Yi/Ki = 1, at 377.6K this is 1.1598 and at 388.8K \n",
      "# it is 0.9677, by interpolation dew point is found to be\n",
      "Td = 387.                           #K\n",
      "Kip1 = 2.85 \n",
      "Kinb1 = 1.25 \n",
      "Kinp1 = 0.59 \n",
      "yp1 = xp/Kip1 \n",
      "ynb1 = xnb/Kinb1 \n",
      "ynp1 = xnp/Kinp1 \n",
      "print \"(b) The dew point temperature = \",Td,\"K\"\n",
      "print \"concentration of propane at dew point = %.4f\"%yp1\n",
      "print \"concentration of n-butane at dew point = %.4f\"%ynb1\n",
      "print \"concentration of n-pentane at dew point = %.4f\"%ynp1\n",
      "\n",
      "#summation zi / (1 + L/VKi)= 0.45, using trial and error, we find\n",
      "T = 374.6                           #K\n",
      "L = 0.55 \n",
      "V = 0.45 \n",
      "Kip2 = 2.5 \n",
      "Kinb2 = 1.08 \n",
      "Kinp2 = 0.48 \n",
      "t = (xp/(1+L/(V*Kip2)))+(xnb/(1+L/(V*Kinb2))) + (xnp/(1+L/(V*Kinp2))) \n",
      "yp2 = (xp/(1+L/(V*Kip2)))/t \n",
      "ynb2 = (xnb/(1+L/(V*Kinb2)))/t \n",
      "ynp2 = (xnp/(1+L/(V*Kinp2)))/t \n",
      "xp2 = (xp - V * yp2)/L \n",
      "xnb2 = (xnb - V * ynb2)/L \n",
      "xnp2 = (xnp - V * ynp2)/L  \n",
      "print \"(c)Temperature of the mixture = \",T,\"K\"\n",
      "print \"vapour phase concentration of propane = %.4f\"%yp2\n",
      "print \"vapour phase concentration of n-butane = %.4f\"%ynb2\n",
      "print \"vapour phase concentration of n-pentane = %.4f\"%ynp2\n",
      "print \"liquid phase concentration of propane = %.4f\"%xp2\n",
      "print \"liquid phase concentration of n-butane = %.4f\"%xnb2\n",
      "print \"liquid phase concentration of n-pentane = %.4f\"%xnp2\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) The buuble point temperature =  361.0 K\n",
        "concentration of propane at bubble point =  0.53\n",
        "concentration of n-butane at bubble point =  0.34\n",
        "concentration of n-pentane at bubble point = 0.130\n",
        "(b) The dew point temperature =  387.0 K\n",
        "concentration of propane at dew point = 0.0877\n",
        "concentration of n-butane at dew point = 0.3200\n",
        "concentration of n-pentane at dew point = 0.5932\n",
        "(c)Temperature of the mixture =  374.6 K\n",
        "vapour phase concentration of propane = 0.3696\n",
        "vapour phase concentration of n-butane = 0.4131\n",
        "vapour phase concentration of n-pentane = 0.2173\n",
        "liquid phase concentration of propane = 0.1521\n",
        "liquid phase concentration of n-butane = 0.3893\n",
        "liquid phase concentration of n-pentane = 0.4586\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.13 pageno : 185"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# variables \n",
      "P = 93.30               #kPa   pressure\n",
      "T1 = 353.               #K     temperature\n",
      "T2 = 373.               #K     temperature\n",
      "Pwater1 = 47.98         #kPa   pressure of water\n",
      "Pwater2 = 101.3         #kPa\n",
      "Pliq1 = 2.67            #kPa   pressure of liquid\n",
      "Pliq2 = 5.33            #kPa\n",
      "\n",
      "# Calculation \n",
      "T = T1 + (T2 - T1)*(P - (Pwater1 + Pliq1))/(Pwater2 + Pliq2 - (Pwater1 + Pliq1)) \n",
      "\n",
      "# Result\n",
      "print \"(a)The equilibrium temperature = %.1f K\"%T\n",
      "Pwater = 88.50 \n",
      "y = Pwater * 100 /P \n",
      "print \"(b)Water vapour in vapour mixture = %.2f %%\"%y\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)The equilibrium temperature = 368.2 K\n",
        "(b)Water vapour in vapour mixture = 94.86 %\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.14 pageno : 185"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "from matplotlib.pyplot import *\n",
      "from numpy import *\n",
      "\n",
      "# variables \n",
      "#the three phase temperature is first find out, which comes to be 342K, the\n",
      "#  corresponding Ps1 = 71.18, Ps2 = 30.12\n",
      "T = [342, 343, 348, 353, 363, 373] \n",
      "Ps2 = [30.12, 31.06, 37.99, 47.32, 70.11, 101.3] \n",
      "Ps1 = [71.18, 72.91, 85.31, 100.5, 135.42, 179.14] \n",
      "P = 101.3                   #kPa\n",
      "\n",
      "y1 = zeros(6)\n",
      "y2 = zeros(6)\n",
      "\n",
      "# Calculation \n",
      "for i in range(6):\n",
      "    y1[i] = 1 - (Ps1[i])/P \n",
      "\n",
      "for i in range(6):\n",
      "    y2[i] = 1 - (Ps2[i])/P \n",
      "\n",
      "# Result\n",
      "plot(y2,T) \n",
      "plot(1-y1,T) \n",
      "suptitle(\"temperature composition diagram\")\n",
      "xlabel(\"x,y mole fraction of benzene\")\n",
      "ylabel(\"Temperature\")\n",
      "show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['draw_if_interactive']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yJezYAXq91mmE+GtGs5HR347mesZ1NoRukOKgsWLv5uro6EizZs1ITEx8qGCi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\nUMEW8YQQQuTDZpeYkpKSGD16NEopDAY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       "text": [
        "<matplotlib.figure.Figure at 0x27c4950>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.15 pageno : 188"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables \n",
      "T = 379.2               #K   solution\n",
      "P = 101.3               #kPa \n",
      "Ps = 70.                #kPa solution\n",
      "Molality = 5\n",
      "\n",
      "# Calculation \n",
      "Pws = math.exp(16.26205 - 3799.887/(T - 46.854)) \n",
      "k = P / Pws \n",
      "Pws1 = Ps / k \n",
      "T1 = 3799.887 / (16.26205 - math.log( Pws1)) + 46.854 \n",
      "\n",
      "# Result \n",
      "print \"Boiling point of the solution = %.1f K\"%T1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Boiling point of the solution = 368.8 K\n"
       ]
      }
     ],
     "prompt_number": 33
    }
   ],
   "metadata": {}
  }
 ]
}